A wall-climbing machining robot curved surface motion control method and system

Abstract

The application belongs to the technical field of industrial robots, and discloses a wall-climbing machining robot curved surface motion control method and system, which comprises the following steps: (1) establishing a robot kinematics model under the constraint of instantaneous motion plane; (2) regarding the model error caused by the kinematics model uncertainty and external disturbance as an extended state, then constructing an extended state observer to observe the kinematics model error of the robot, and obtaining an error compensation control signal; on the basis of not considering the kinematics uncertainty, establishing a kinematics error state space model of the robot trivial system, and establishing a nonlinear model predictive controller, then solving the optimal control sequence of a cost function to obtain the control signal of the trivial system; (3) calculating the control signal of the closed-loop control system of the robot, and then realizing the motion control of the wall-climbing machining robot on the curved surface in three-dimensional space. The application provides protection for efficient and high-precision machining of the wall-climbing machining robot.

Description

Technical Field

[0001] This invention belongs to the field of industrial robot technology, and more specifically, relates to a method and system for controlling the curved surface motion of a wall-climbing processing robot. Background Technology

[0002] Wall-climbing machining robots, capable of adhering to and machining the surfaces of large and complex components, offer a new machining method for large and complex parts such as aircraft skins, ship hulls, and wind turbine blades. High-precision motion control is the guarantee for wall-climbing machining robots to perform efficient and high-precision machining on workpiece surfaces.

[0003] Large and complex components typically have free-form surfaces with varying curvature. Due to these variations in curvature, the contact state between the robot's wheels and the surface changes in real time as the robot moves across the curved surface. This makes it difficult to establish an accurate kinematic model for the robot's movement on the surface. Furthermore, during movement, the friction between the robot's wheels and the workpiece surface is insufficient to counteract the drag caused by gravity, leading to slippage. Therefore, the robot is subject to significant external disturbances during its movement. These issues pose a challenge to the high-precision motion control of wall-climbing robots on curved surfaces. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a surface motion control method and system for wall-climbing processing robots, which can realize high-precision motion of wall-climbing processing robots on large and complex components, and provide a guarantee for the efficient and high-precision processing of wall-climbing processing robots.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for controlling the surface motion of a wall-climbing processing robot is provided, the method comprising the following steps:

[0006] (1) Obtain the instantaneous motion plane during the robot's motion process and establish the robot's kinematic model under the constraints of the instantaneous motion plane;

[0007] (2) The kinematic model uncertainty and the model error introduced by external disturbance are regarded as the extended state. An extended state equation is established, and then an extended state observer is constructed to observe the kinematic model error of the robot and obtain the error compensation control signal. At the same time, without considering the kinematic uncertainty, a kinematic error state space model of the robot's trivial system is established based on the leader-follower configuration of the robot. A nonlinear model predictive controller is established based on the kinematic error state space model, and then the optimal control sequence of the cost function is solved to obtain the control signal of the trivial system.

[0008] (3) Based on the error compensation control signal and the control signal of the trivial system, calculate the control signal of the robot's closed-loop control system, and then realize the motion control of the wall-climbing processing robot on the three-dimensional curved surface.

[0009] Furthermore, the instantaneous motion plane is the plane formed by the contact points between the robot's wheel train and the workpiece surface during the motion, and the constraints of the instantaneous motion plane are:

[0010] c(x) = [v z ω x ω y ] T =0

[0011] Where v z Let ω be the linear velocity in the z-direction of the robot's body coordinate system. x and ω y These are the rotational angular velocities in the x and y directions, respectively, in the robot's body coordinate system.

[0012] Furthermore, under the constraint of the instantaneous motion plane, the expression for the kinematic model of the robot on the instantaneous motion plane is:

[0013]

[0014] Where q=[ξ T υ T ] T Let ξ be the state variable of the system, where ξ = [x, y, z]. T and υ=[φθψ] T These represent the Cartesian coordinates of the robot's body coordinate system in the inertial coordinate system and the RPY attitude angle, respectively; t is time. To control the input signal, v x and v y Let ω be the linear velocity in the x and y directions, respectively, in the robot's body coordinate system. z Let be the rotational angular velocity in the z-direction of the robot's body coordinate system. For kinematic model error; Let be the state transition matrix, where c(·), s(·), and t(·) are abbreviations for the cosine, sine, and tangent trigonometric functions, respectively.

[0015] Furthermore, the spatial equation for the extended state is:

[0016]

[0017] Where x1(t) = q(t) are the state variables of the system, and x2(t) = d(t) are the extended state variables;

[0018] The extended state observer designed based on the extended state-space equation is:

[0019]

[0020] in For system state variable x i The observed values ​​of (t)(i=1,2), is the observer gain coefficient.

[0021] Furthermore, the gain coefficients of the observer are tuned using the pole placement method, and the characteristic polynomial of the observer is:

[0022] Λ(s)=s 2 I + β1s + β2 = (s + ω0) 2 I

[0023] Where I is the identity matrix and ω0 is the adjustable observer bandwidth, the gain coefficients of the extended state observer are β1 = 2ω0I and β2 = ω0. 2 I;

[0024] The error compensation control signal is:

[0025]

[0026] in, It is the left generalized inverse of the state transition matrix. These are the observed values ​​of the kinematic model error.

[0027] Furthermore, the kinematic error state-space model is decoupled into position error and attitude error state-space models; the differential equation for the position error state variable is:

[0028]

[0029] Among them, the position error state variable Let x be the x-coordinate of the leader robot in the body coordinate system of the follower robots. Let y be the leader robot's y-coordinate in the follower robot's body coordinate system; v xf and v yf Let v be the linear velocity in the x and y directions, respectively, of the follower robot's body coordinate system. xr and v yr These represent the linear velocities in the x and y directions, respectively, within the leader robot's body coordinate system. R r and R f These are the rotation transformation matrices for the leader and follower robots, respectively.

[0030] Furthermore, the differential equation for the attitude error state variable is:

[0031]

[0032] Where, ω r As the ideal angular velocity control variable, it is kept constant at zero in this embodiment. zf Let be the robot's angular velocity control variable; the expression for the robot's kinematic error state-space model is:

[0033]

[0034] in For state variables, For position error state variables, The attitude error state variable; To construct control signal variables, ω is the linear velocity control variable. zf This is the angular velocity control variable.

[0035] Furthermore, the expression for the nonlinear model predictive controller is:

[0036]

[0037] st

[0038] q f (t|t)=q f (t)

[0039]

[0040]

[0041]

[0042]

[0043] in For stage cost function, Let P and R be the terminal cost function, where P and R are positive definite symmetric matrices; for Time error state variables The predicted value, for Constructing the control signal variable at time q f u represents the actual state variable of the follower in three-dimensional space. f For the control input signals of the robot, To control the input signal constraints, T p To control the time domain, α and ε are positive constants. For terminal constraints.

[0044] Furthermore, the optimal solution of the objective function is obtained by solving... Obtain the optimal control sequence The control signal predicted by the nonlinear model of a trivial system is the first term of the optimal sequence.

[0045] This invention also provides a surface motion control system for a wall-climbing machining robot. The system includes a model building module, a control signal acquisition module, and a closed-loop control module. The model building module acquires the instantaneous motion plane during the robot's motion and establishes a kinematic model of the robot under the constraints of the instantaneous motion plane. The control signal acquisition module treats the model errors introduced by kinematic model uncertainties and external disturbances as extended states, establishes extended state equations, and then constructs an extended state observer to observe the robot's kinematic model errors, obtaining error compensation control signals. It also establishes a kinematic error state-space model of the robot's trivial system based on the leader-follower configuration of the robot, without considering kinematic uncertainties, and establishes a nonlinear model predictive controller based on the kinematic error state-space model, thereby solving for the optimal control sequence of the cost function and obtaining the control signals of the trivial system. The closed-loop control module calculates the control signals of the robot's closed-loop control system based on the error compensation control signals and the control signals of the trivial system, thus realizing the motion control of the wall-climbing machining robot on a three-dimensional curved surface.

[0046] In summary, compared with the prior art, the surface motion control method and system for wall-climbing processing robots provided by this invention have the following advantages:

[0047] 1. This invention establishes a kinematic model of a wall-climbing machining robot moving on free-form surfaces such as large and complex components based on instantaneous planar real-time projection and a leader-follower model. It effectively solves the challenges brought about by the kinematic model of moving on free-form surfaces with varying curvature, and effectively solves the challenges brought about by the real-time change of the geometric contact state between the robot and the surface when moving on free-form surfaces with varying curvature. It realizes the establishment and correction of an accurate kinematic model of the wall-climbing machining robot moving on the surface.

[0048] 2. By introducing an extended state observer to observe and compensate for kinematic model errors based on nonlinear model predictive control, the robustness of the closed-loop control system is further improved, showing a significant advantage in situations where the robot is subjected to large external disturbances due to slippage. Attached Figure Description

[0049] Figure 1 This is a control block diagram of the surface motion control method for a wall-climbing processing robot provided by the present invention;

[0050] Figure 2 This is a schematic diagram of the wall-climbing processing robot in this embodiment;

[0051] Figure 3 This is a schematic diagram of the instantaneous motion plane of a wall-climbing machining robot during curved surface motion;

[0052] Figure 4 This is a leader-follower diagram of the curved surface motion of a wall-climbing machining robot;

[0053] Figure 5 This is a diagram showing the motion trajectory of a wall-climbing processing robot as it moves across a curved surface.

[0054] Figure 6 (a) and (b) in the figure are tracking error diagrams of the wall-climbing processing robot when it moves on the curved surface;

[0055] Figure 7 (a) and (b) are control signal diagrams of the trivial system when the wall-climbing processing robot moves on the curved surface. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0057] Please see Figure 1 This invention provides a surface motion control method for a wall-climbing machining robot. The method first establishes the robot's kinematic equations under instantaneous plane constraints based on real-time projection onto an instantaneous plane. Further, an extended state observer is constructed to observe the kinematic errors during the robot's motion, and error compensation control signals are generated to improve the robustness of the closed-loop control system. Further, a robot kinematic error state equation for a trivial system is constructed based on a leader-follower configuration. Based on this kinematic state error model, nonlinear model predictive control is used to obtain the control signal for the trivial system. Further, the control signal for the closed-loop system, obtained based on the error compensation control signal and the nonlinear model predictive control signal for the trivial system, is applied to the robot, achieving high-precision motion control of the wall-climbing machining robot on the surface of large and complex components.

[0058] The control method mainly includes the following steps:

[0059] S1: Obtain the instantaneous motion plane during the robot's motion process and establish the robot's kinematic model under the constraints of the instantaneous motion plane.

[0060] As shown in Figure 2, the wall-climbing processing robot in this embodiment includes a vacuum adsorption type wall-climbing processing robot platform comprising three omnidirectional drive wheels 11 evenly distributed at 120 degrees and three flexible adsorption chambers 12 evenly distributed at 120 degrees. Figure 3 As shown, the instantaneous motion plane is the plane 3 formed by the three contact points between the robot wheel train 1 and the workpiece surface 2 during the motion.

[0061] The constraints on the instantaneous motion plane are:

[0062] c(x) = [v z ω x ω y ] T =0

[0063] Where v z Let ω be the linear velocity in the z-direction of the robot's body coordinate system. x and ω y These are the rotational angular velocities in the x and y directions, respectively, in the robot's body coordinate system.

[0064] Under the constraint of the instantaneous motion plane, the expression of the kinematic model of the robot on the instantaneous motion plane is:

[0065]

[0066] Where q=[ξ T υ T ] T Let ξ be the state variable of the system, where ξ = [x, y, z]. T and υ=[φθψ] T These represent the Cartesian coordinates of the robot's body coordinate system in the inertial coordinate system and the RPY attitude angle, respectively; t is time. To control the input signal, v x and v y Let ω be the linear velocity in the x and y directions, respectively, in the robot's body coordinate system. z Let be the rotational angular velocity in the z-direction of the robot's body coordinate system. For kinematic model error; Let be the state transition matrix, where c(·), s(·), and t(·) are abbreviations for the cosine, sine, and tangent trigonometric functions, respectively.

[0067] S2 treats the kinematic model uncertainty and the model error introduced by external disturbances as an extended state, establishes an extended state equation, and then constructs an extended state observer to observe the robot's kinematic model error and obtain the error compensation control signal.

[0068] Treating the model errors introduced by kinematic model uncertainties and external disturbances as an extended state, the spatial equation of the extended state is constructed as follows:

[0069]

[0070] Where x1(t)=q(t) are the state variables of the system, and x2(t)=d(t) are the extended state variables.

[0071] The extended state observer designed based on the extended state-space equation is:

[0072]

[0073] in For system state variable x i The observed values ​​of (t)(i=1,2), Let i be the observer gain coefficient, i = 1, 2.

[0074] The gain coefficient of the observer is tuned using the pole placement method, and the characteristic polynomial of the observer is:

[0075] Λ(s)=s 2 I + β1s + β2 = (s + ω0) 2 I

[0076] Where I is the identity matrix and ω0 is the adjustable observer bandwidth, the gain coefficients of the extended state observer are β1 = 2ω0I and β2 = ω0. 2 I.

[0077] The error compensation control signal is:

[0078]

[0079] in, It is the left generalized inverse of the state transition matrix. These are the observed values ​​of the kinematic model error.

[0080] S3. Without considering kinematic uncertainties, a kinematic error state space model of the robot's trivial system is established based on the leader-follower configuration corresponding to the robot.

[0081] The kinematic error state space model is decoupled into position error and attitude error state space models.

[0082] Please see Figure 4 The differential equation for the position error state variable is:

[0083]

[0084] Among them, the position error state variable Let x be the x-coordinate of the leader robot in the body coordinate system of the follower robots. Let y be the leader robot's y-coordinate in the follower robot's body coordinate system; v xf and v yf Let v be the linear velocity in the x and y directions, respectively, of the follower robot's body coordinate system. xr and v yr These represent the linear velocities in the x and y directions, respectively, within the leader robot's body coordinate system. R r and R f These are the rotation transformation matrices for the leader and follower robots, respectively.

[0085] The differential equation for the attitude error state variable is:

[0086]

[0087] Where, ω r As the ideal angular velocity control variable, it is kept constant at zero in this embodiment. zf This is the robot's angular velocity control variable.

[0088] Based on the differential equations of the position and attitude error state variables mentioned above, the expression for the robot's kinematic error state-space model is as follows:

[0089]

[0090] in For state variables, For position error state variables, The attitude error state variable; To construct control signal variables, ω is the linear velocity control variable. zf This is the angular velocity control variable.

[0091] S4. A nonlinear model predictive controller is established based on the kinematic error state-space model, and then the optimal control sequence of the cost function is solved to obtain the control signal of the trivial system.

[0092] The expression for the nonlinear model predictive controller is:

[0093]

[0094] st

[0095] q f (t|t)=q f (t)

[0096]

[0097]

[0098]

[0099]

[0100] in For stage cost function, Let P and R be the terminal cost function, where P and R are positive definite symmetric matrices; for Time error state variables The predicted value, for Constructing the control signal variable at time q f u represents the actual state variable of the follower in three-dimensional space. f For the control input signals of the robot, To control the input signal constraints, T p To control the time domain, α and ε are positive constants. For terminal constraints.

[0101] By solving the optimal solution of the objective function Obtain the optimal control sequence The control signal predicted by the nonlinear model of a trivial system is the first term of the optimal sequence.

[0102] In this embodiment, the controller parameters are set as follows: δ = 0.1s, T p =10δ=1s, α=0.01, P=diag(5.0,5.0,5.0), R=diag(0.1,0.1,0.1).

[0103] S5 calculates the control signal of the robot's closed-loop control system based on the error compensation control signal and the control signal of the trivial system, thereby realizing the motion control of the wall-climbing processing robot on the three-dimensional curved surface.

[0104] The expression for the control signal of the closed-loop system is:

[0105] u(t)=κ(u f (t),u d (t))=u f (t)-u d (t)

[0106] Where u f (t) represents the nonlinear model predictive control signal of the trivial system, u d (t) is the error compensation control signal for the extended state observer.

[0107] Based on the aforementioned closed-loop system control signals, the robot achieved high-precision motion control on the curved surface of the wind turbine blade. In the convergent state, the average trajectory tracking error was less than 0.1 mm, and the root mean square error was less than 2 mm. The motion trajectory diagram is shown below. Figure 5 As shown, the tracking error graph is as follows: Figure 6 As shown, the control signal diagram of a trivial system is as follows: Figure 7 As shown, the surface motion control method for wall-climbing machining robots based on extended state observer and nonlinear model predictive control has good tracking accuracy and robustness.

[0108] In another embodiment, the control method is executed according to the above steps S1, S3, S4, S2 and S5; of course, steps S3-4 and step S2 can be performed simultaneously.

[0109] This invention also provides a surface motion control system for a wall-climbing machining robot. The system includes a model building module, a control signal acquisition module, and a closed-loop control module. The model building module acquires the instantaneous motion plane during the robot's motion and establishes a kinematic model of the robot under the constraints of the instantaneous motion plane. The control signal acquisition module treats the model errors introduced by kinematic model uncertainties and external disturbances as extended states, establishes extended state equations, and then constructs an extended state observer to observe the robot's kinematic model errors, obtaining error compensation control signals. It also establishes a kinematic error state-space model of the robot's trivial system based on the leader-follower configuration of the robot, without considering kinematic uncertainties, and establishes a nonlinear model predictive controller based on the kinematic error state-space model, thereby solving for the optimal control sequence of the cost function and obtaining the control signals of the trivial system. The closed-loop control module calculates the control signals of the robot's closed-loop control system based on the error compensation control signals and the control signals of the trivial system, thereby realizing the motion control of the wall-climbing machining robot on a three-dimensional curved surface.

[0110] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the surface motion of a wall-climbing machining robot, characterized in that, The method includes the following steps: (1) Obtain the instantaneous motion plane during the robot's motion process and establish the robot's kinematic model under the constraints of the instantaneous motion plane; (2) The kinematic model uncertainty and the model error introduced by external disturbance are regarded as the extended state. The extended state equation is established, and then the extended state observer is constructed to observe the kinematic model error of the robot and obtain the error compensation control signal. At the same time, without considering the kinematic uncertainty, the kinematic error state space model of the robot's trivial system is established based on the leader-follower configuration of the robot, and a nonlinear model predictive controller is established based on the kinematic error state space model. Then, the optimal control sequence of the cost function is solved to obtain the control signal of the trivial system. (3) Based on the error compensation control signal and the control signal of the trivial system, calculate the control signal of the robot's closed-loop control system, and then realize the motion control of the wall-climbing processing robot on the three-dimensional space surface; The kinematic error state-space model is decoupled into position error and attitude error state-space models; the differential equation of the position error state variable is: Among them, the position error state variable , Let x be the x-coordinate of the leader robot in the body coordinate system of the follower robots. Let y be the leader robot's y-coordinate in the follower robot's body coordinate system; , and These are the linear velocities in the x and y directions, respectively, in the follower robot's body coordinate system. and These represent the linear velocities in the x and y directions, respectively, within the leader robot's body coordinate system. , , and These are the rotation transformation matrices for the leader and follower robots, respectively; The differential equation for the attitude error state variable is: in, As the ideal angular velocity control variable, it is kept constant at zero. Let be the robot's angular velocity control variable; the expression for the robot's kinematic error state-space model is: in For state variables, For position error state variables, The attitude error state variable; To construct control signal variables, For linear velocity control variables, This is the angular velocity control variable.

2. The surface motion control method for a wall-climbing processing robot as described in claim 1, characterized in that: instantaneous The motion plane is the plane formed by the contact points between the robot's wheel train and the workpiece surface during motion. The constraints of the instantaneous motion plane are: in Let be the linear velocity in the z-direction in the robot's body coordinate system. and These are the rotational angular velocities in the x and y directions, respectively, in the robot's body coordinate system.

3. The surface motion control method for a wall-climbing processing robot as described in claim 2, characterized in that: Under the constraint of the instantaneous motion plane, the expression of the kinematic model of the robot on the instantaneous motion plane is: in Let be the state variables of the system, where and These represent the Cartesian coordinates of the robot's body coordinate system in the inertial coordinate system and the RPY attitude angle, respectively. For time; To control the input signal, and These are the linear velocities in the x and y directions, respectively, in the robot's body coordinate system. Let be the rotational angular velocity in the z-direction of the robot's body coordinate system. For kinematic model error; This is the state transition matrix. , and These are abbreviations for cosine, sine, and tangent trigonometric functions, respectively.

4. The surface motion control method for a wall-climbing processing robot as described in claim 1, characterized in that: The spatial equation for the extended state is: in, For the system's state variables, For expanding state variables; The extended state observer designed based on the extended state-space equation is: in System state variables The observed values, The observer gain coefficient, .

5. The surface motion control method for a wall-climbing processing robot as described in claim 4, characterized in that: The gain coefficient of the observer is tuned using the pole placement method, and the characteristic polynomial of the observer is: in, It is the identity matrix. Given an adjustable observer bandwidth, the gain coefficient of the extended state observer is: , ; The error compensation control signal is: in, It is the left generalized inverse of the state transition matrix. These are the observed values ​​of the kinematic model error.

6. The surface motion control method for a wall-climbing processing robot as described in claim 1, characterized in that: The expression for the nonlinear model predictive controller is: in For stage cost function, For terminal cost function, and It is a positive definite symmetric matrix; for Time error state variables The predicted value, for The construction of control signal variables at time points, For the actual state variables of the followers in three-dimensional space For the control input signals of the robot, To control input signal constraints, To control the time domain, and For positive integers, For terminal constraints.

7. The surface motion control method for a wall-climbing processing robot as described in claim 6, characterized in that: By solving the optimal solution of the objective function To obtain the optimal control sequence The nonlinear model predicts the control signal of a trivial system as the first term of the optimal sequence.

8. A surface motion control system for a wall-climbing processing robot, characterized in that: The system includes a model building module, a control signal acquisition module, and a closed-loop control module. The model building module acquires the instantaneous motion plane during the robot's movement and establishes a robot kinematic model constrained by the instantaneous motion plane. The control signal acquisition module treats the model errors introduced by kinematic model uncertainties and external disturbances as extended states, establishes extended state equations, and then constructs an extended state observer to observe the robot's kinematic model errors, obtaining error compensation control signals. It also establishes a kinematic error state-space model of the robot's trivial system based on the leader-follower configuration of the robot, without considering kinematic uncertainties, and establishes a nonlinear model predictive controller based on the kinematic error state-space model, thereby solving for the optimal control sequence of the cost function and obtaining the control signals of the trivial system. The closed-loop control module calculates the control signals of the robot's closed-loop control system based on the error compensation control signals and the control signals of the trivial system, thus realizing the motion control of the wall-climbing processing robot on a three-dimensional curved surface. The kinematic error state-space model is decoupled into position error and attitude error state-space models; the differential equation of the position error state variable is: Among them, the position error state variable , Let x be the x-coordinate of the leader robot in the body coordinate system of the follower robots. Let y be the leader robot's y-coordinate in the follower robot's body coordinate system; , and These are the linear velocities in the x and y directions, respectively, in the follower robot's body coordinate system. and These represent the linear velocities in the x and y directions, respectively, within the leader robot's body coordinate system. , , and These are the rotation transformation matrices for the leader and follower robots, respectively; The differential equation for the attitude error state variable is: in, As the ideal angular velocity control variable, it is kept constant at zero. Let be the robot's angular velocity control variable; the expression for the robot's kinematic error state-space model is: in For state variables, For position error state variables, The attitude error state variable; To construct control signal variables, For linear velocity control variables, This is the angular velocity control variable.

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